Dynamics and density function for a stochastic anthrax epidemic model

Abstract

In response to the pressing need to understand anthrax biology, this paper focused on the dynamical behavior of the anthrax model under environmental influence. We defined the threshold parameter $ R^s $, when $ R^s > 1 $; the disease was almost certainly present and the model exists a unique ergodic stationary distribution. Subsequently, statistical features were employed to analyze the dynamic behavior of the disease. The exact representation of the probability density function in the vicinity of the quasi-equilibrium point was determined by the Fokker-Planck equation. Finally, some numerical simulations validated our theoretical results.

Keywords

• stochastic anthrax model
• ergodic stationary distribution
• fokker-planck equation
• probability density function